# How do you find the domain of f(x)= sqrt(x+6)/(x-5)?

##### 1 Answer
Apr 21, 2015

For this function to have a value we need to satisfy two conditions:
(a) an expression under the sign of a square root should not be negative, that is $x + 6 \ge 0$;
(b) an expression in the denominator should not be equal to $0$, that is $x - 5 \ne 0$.

The first condition resolves into
(a) $x \ge - 6$
The second one resolves into
(b) $x \ne 5$

Therefore, the domain of $f \left(x\right) = \frac{\sqrt{x + 6}}{x - 5}$ consists of two segments:
$- 6 \le x < 5$ and $x > 5$